 Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4734. (October 2015)

B. 4734. Some fields (unit cubes) constituting a cubical lattice of edge 2015 units are infected by an unknown disease. The disease will spread if at least $\displaystyle t$ fields in some row parallel to any edge of the cube are infected $\displaystyle (1 \le t \le 2015)$. In that case, every field of that row will become infected in one minute. How many fields need to be infected initially in order to

$\displaystyle a)$ make it possible

$\displaystyle b)$ be certain

that the infection reaches all fields of the cube?

Proposed by G. Mészáros, Budapest

(6 pont)

Deadline expired on November 10, 2015.

### Statistics:

 61 students sent a solution. 4 points: 12 students. 3 points: 10 students. 2 points: 14 students. 1 point: 15 students. 0 point: 8 students. Unfair, not evaluated: 2 solutionss.

Problems in Mathematics of KöMaL, October 2015